5.1 Transformations
Define the parameters a, h, and k from the general function g(x)=a(x-h)3+k.
What is,
a- stretch factor
h- horizontal shift
k- vertical shift
Given the set of points {(0,1), (3,2), (5,1)} find the inverse set.
What is, {(1,0), (2,3), (1,5)}.
How many x-intercepts do cubic functions have?
What is, only one intercept.
Is the following polynomial odd or even?
f(x)=x(x+3)2
What is, odd.
Describe the difference between horizontal shift and vertical shift.
What is, horizontal shifts left and right while vertical shifts up and down.
Describe the transformations: h(x)=5(x+1)2
What is, vertical stretch of 5 and shift left 1.
True or false: the point (-3,5) is the inverse of (5,-3).
What is, true.
Where is reference point number 1 always located?
What is, in the middle.
Describe the end behavior of this polynomial:
g(x)= -x(x-4)(x+2)2
What is, even/negative. (arrows down on both sides)
How can you tell if a polynomial is positive or negative?
What is, the leading coefficient.
True or false: the function f(x)=-x2+3 displays a reflection on the y-axis and a vertical shift up 3 units.
What is, false.
Find the inverse function, f-1(x), to the function f(x)=3x-4.
What is, f-1(x)=(x+4)/3.
What are the coordinates to the 3 reference points needed to graph cubic function?
What is, #1 (h,k) #2 (h+1,k+a) #3 (h-1,k-a).
True or false: this polynomial is degree 5.
g(x)= -(x+3)2(x-3)2
What is, false.
Describe the 4 different types of end behavior.
What is, odd/positive, odd/negative, even/positive, even/negative.
Shift the coordinate (1,2) 5 units up and 3 units left. What is the resulting coordinate?
What is, (-2,7).
Find the inverse function, f-1(x), to the function f(x)=(3/5)x+2
What is, f-1(x)=(5/3)x-(10/3)
Given the cubic function f(x)=-4(x+2)3-1, find the three reference coordinates.
What is, #1 (-2,-1) #2 (-1,-5) #3 (-3,3)
List the x-intercepts for this polynomial:
h(x)=x(x+5)(x-3)
What is, x=0,3,-5
Describe the difference between finding the degree of a polynomial in standard form vs. factored form.
What is, in standard form the degree is the value of the largest exponent and in factored form you find the sum of all the exponents.
Write an equation for a cubic function that is reflected on the x-axis, vertically stretched by a factor of 4, shifted 7 units right, and shifted 2 units down.
What is, g(x)=-4(x-7)3-2
What line are inverse functions reflected on?
What is, the line y=x.
Write the end behavior of an odd positive function using the formal definition.
What is,
as x--00, f(x)--00
as x-- -00, f(X)-- -00
Determine if the graph is tangent or crosses at each intercept.
f(x)=x2(x+4)(x-3)2
What is, tangent at 0/cross at -4/tangent at 3.
What is the difference between vertical stretch and vertical compression?
What is, vertical stretch when a>1 or a<-1 and vertical compression when a is a fraction 0<a<1.